All Questions

Let $f(x)=\sum_{n\geq 1} c_n\cdot x^n$ be a function given by a power series. Further there is some $\alpha >1$ such that for all $n$, $c_n = \Theta(1/n^{\alpha})$. What can one say about the ...

Let $(a_n)$ be a sequence of real numbers, and suppose that the real power series (function) $S(x):=\sum_{n=0}^{\infty} a_n x^n$ converges for every $x\in\mathbb{R}$. $\mathbf{Question}$: Suppose ...

There's a formula for the $n$th derivative of a composite function $f(g(x))$ - it's called Faa di Bruno's formula - but I'm not really interested in the formula but in the proof given in the book of ...